ULTRA HIGH STRAIN RATE
Although the nanoindentation technique has evolved in recent years, most tests are still typically performed in the quasi-static regime, meaning at strain rates in the range of 10-5 to 10-2 s-1. Some efforts to investigate dynamic material properties have led to the development of dynamic mechanical analysis (DMA) which typically applies a sinusoidal signal to the loading curve and relies on the phase shift of the resultant displacement signal to extract dynamic properties (such as storage and loss moduli). However, strain rates above 10-2 s-1 have remained unexplored owing to the limitations in conventional nanoindentation instrument design where the resonance frequency of the system is commonly too low to allow for high strain rate experiments.
The behavior of materials at high strain rates is of great interest, both in industrial applications and in fundamental research. Some industrial examples include the impact resistance of ballistic armor, survival of components/devices when dropped, crash testing, metalworking operations, etc. From a scientific viewpoint, being able to test materials over a wide range of strain rate allows the deformation mechanisms to be probed and understood, particularly with regard to determination of activation volumes.
Size scale as a function of strain rate magnitude with existing experimental and simulation areas of activity (Courtesy of Rajaprakash Ramachandramoorthy, EMPA, Thun, Switzerland). Note that DDD = Discrete Dislocation Dynamics, MD = Molecular Dynamics and SLME = Self-Learning Metabasin Escape.
At the macroscale, there are various test systems for the measurement of high strain rate. Conventional servo hydraulic machines are generally used for testing quasi-static strain rates of 1 s-1 or less. With special design, these instruments can attain greater strain rates up to about 100 s-1 with conventional load frames. For much higher strain rates, the most common is the split-Hopkinson (or Kolsky) pressure bar, which allows the deformation of a sample of a ductile material at a high strain rate, while maintaining a uniform uniaxial state of stress within the sample. This apparatus is used to sandwich the sample between an input and an output bar and can reach strain rates up to 104 s-1, although the maximum strain rate that can be attained varies inversely with the length of the test specimen. In addition, this method is limited by the elastic limit of the Hopkinson bars that are used to transmit the stress pulse to the sample.
At the microscale, the main difficulty in achieving high strain rates with conventional nanoindenters is their resonant frequency which is too low and scatters the recorded dataset. In most systems, the feedback loop is often not fast enough to resolve load and displacement at high strain rate, this also being due to the data sampling rates required (> 10 kHz) and the increased signal noise which reduces the accuracy of the results.
The Alemnis Standard Assembly (ASA) can be configured in several ways to achieve ultra high strain rates up to 10’000 s-1, thus covering 8 orders of magnitude! Such high strain rates are possible because the dimensions of a typical micropillar are so small relative to the actuation velocity, the lower magnitude of inertial contributions and faster stress wave equilibration times. For example, the duration of a dynamic experiment conducted at 1000 s-1 strain rate is ̴70 µs for both macro- and microscale samples. If we take fused silica, which has an elastic wave speed of ̴ 5823 ms-1, the wave travel time in a typical macroscale sample of 9 mm thickness (typical Kolsky bar sample thickness is 6 – 12 mm) is ̴ 2 µs, while the wave travel time in a 5 µm high micropillar of the same material is 1 ns. Thus, at the macroscale, the experiment duration is of the same order of magnitude as the wave travel time, so understanding the wave propagation phenomena is vital (and in practice very complicated). On the other hand, at the microscale, the experiment duration far exceeds the wave travel time, essentially making the wave propagation phenomena irrelevant in such samples at strain rates less than ̴ 105 s-1. Therefore, in dynamic micromechanical testing, the elastic and plastic constitutive material properties of microscale samples can be obtained at very high strain rates without interference from the elastic waves in the material. This means that exploring the high strain rate mechanical properties at the microscale is very advantageous compared to the macroscale.
The four ASA configurations for high strain rate testing
The four possible configurations for high strain rate testing are summarized in the table, where SmarTip actuators can be mounted either on the displacement head side (all four configurations) or also on the sample side. The resonance frequency of the ASA is of the order of > 10 kHz, depending on the actual configuration. Different SmarTips are available, either in single or 3-axis configuration. For example:
- VHS-1-1 configuration: the displacement is made by the piezostack actuator and the resultant load is measured by the SmarTip (note that the SmarTip could also be mounted under the sample in this configuration), allowing very high strain rates up to 1000 s-1. Typical application is high strain rate testing, fatigue, impact, dynamic, etc.
- UHS-1-1 configuration: two SmarTips are mounted either side of the sample, where one is the actuator and the other the sensor. This allows even higher strain rates up to 10’000 s-1. Typical application is ultra high strain rate testing, fatigue, impact, dynamic, etc.
- UHS-1-3 and UHS-3-3 configurations: these are the same as for UHS-1-1, except that either one or both SmarTips are capable of actuation/sensing in 3 axes (normal Z axis and two lateral XY axes). Typical application is ultra high strain rate testing, fatigue, impact, dynamic, as well as scratch testing, tribology, fretting, lateral oscillation, etc.
The SmarTip actuator is powered by a state-of-the-art high voltage, high speed amplifier capable of inputting high voltages across a variety of time scales with very high slew rates. The embedded strain gauges are capable of capturing these high speed displacements with a resolution of ̴15 nm. The displacement voltage signals are acquired using a data acquisition board capable of high speed sampling up to 50’000 samples per second. When using the SmarTip as a load sensor, it can sense changes in load at high frequencies up to 10 kHz with a resolution of 30 µN. For load signals at strain rates < 1 s-1, the high speed acquisition up to 50’000 samples per second is more than adequate. For tests at higher strain rates (> 1 s-1) the amplified load signal from the charge amplifier is captured using an oscilloscope to acquire a non-aliased signal using its ultra high sampling rates of up to 2.5 giga samples per second. The load and displacement signals are then time synchronized to obtain the final load-displacement curve, from which the stress-strain curves can be derived using the top cross-sectional area of the micropillar and its height, respectively. Given that the majority of the deformation is focused in the top third of the micropillar, even at very high strains, the assumption of using the top cross-section to obtain the stress remains valid.
Another advantage of using the high-stiffness SmarTip actuator and SmarTip load sensor in combination with a stiff frame (e.g., UHS-1-1 configuration), for high strain rate tests, is that the combined machine compliance is reduced to a very low value, of the order of 10-7 m/N. This means that the high strain rate tests are essentially conducted at intrinsic displacement control, thus allowing a precise strain to be induced in the micropillar. In practice, the high strain rate test can therefore be stopped at a predefined strain and the sample allowed to recover, after which direct examination with SEM or TEM is possible to understand better the deformation mechanism.
A particularly interesting case study is summarized here, based on the seminal work of Dr. Rajaprakash Ramachandramoorthy et al (Ref. 3) who has studied fused silica (glass) at strain rates which span 8 orders of magnitude and uncovered a remarkable ductile-brittle-ductile failure mode transition at increasing strain rates from 0.0008 to 1335 s-1 as the deformation flow transitions between homogeneous-serrated-homogeneous regimes. Before this study, published in 2019, the mechanical properties of fused silica had only ever been investigated up to maximum strain rates of < 0.02 s-1 so the potential of the Alemnis system to increase knowledge of materials at high strain rates is undeniable!
Amorphous silica micropillars strained to 20% at strain rates of 0.07, 0.7, 50 and 500/s (scale bar: 2 µm). The surface of the micropillars tested at each strain rate are magnified to show the surface steps left by shear band propagation (scale bar: 250 nm) (from Ref. 3)
Amorphous materials such as fused silica do not have long-range order, unlike their crystalline counterparts (quartz), and their exact deformation mechanisms are not clearly understood, although the fundamental unit process is thermally activated local rearrangement of atoms that can accommodate shear strain. Serrated flow is observed in fused silica micropillars at intermediate strain rates of 0.07 to 6 s-1 and close investigation of their surfaces reveals multiple shear-band propogations that manifest as surface steps on the pillar. The ratio of the shear band propagation speed to the actuation speed used in the experiment at different strain rates in the serrated regime can be plotted against the plastic strain.
Dependence of plastic strain on the ratio between the shear-band propagation speed and the actuation speed across the three different strain rates in the serrated regime (from Ref. 3)
It can clearly be seen that when the ratio is kept low, between 1 and 5, significant plastic strain can be achieved in the fused silica micropillars because a controlled progression of shear band nucleation, propagation and further slip on the shear band can be achieved. On the contrary, when the ratio is greater than 5, the micropillar cannot sustain a stable plasticity and becomes brittle.
Rate-dependent response of silica micropillars subjected to strain rates from 0.07/s up to 1335/s with their corresponding stress-strain curves from 0.0008/s up to 1335/s (from Ref. 3)
In summary, fused silica micropillars exhibit strong rate-dependent mechanical properties, including yield strength and plastic strain. The deformation mechanisms behind such rate-dependent properties also vary significantly depending on the flow regime. As such, at lower strain rates, shear-band propagation kinetics dictate the flow, while at higher strain rates, shear-band nucleation kinetics dominate because individual shear-band propagations cannot accommodate the applied strain quickly enough to relieve the high stress levels.
A similar methodology to that presented here for fused silica micropillars could be applied to a whole host of other materials whose high strain rate properties have never been investigated. Other amorphous materials such as bulk metallic glasses, amorphous glassy carbon, etc. are of great interest if their deformation behaviors can be measured at extreme, yet application-relevant, conditions. High strain rate micromechanical experiments will help to bridge the gap between experiments and atomistic simulations, which can lead to the accelerated design and discovery of functional materials with tunable physical properties.
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- G. Guillonneau, M. Mieszala, J. Wehrs, J. Schwiedrzik, S. Grop, D. Frey, L. Philippe, J-M. Breguet, J. Michler, J. M. Wheeler, Nanomechanical testing at high strain rates: new instrumentation for nanoindentation and microcompression, Materials and Design 148 (2018) 39-48
- R. Ramachandramoorthy, J. Schwiedrzik, L. Petho, C. Guerra-Nunez, D. Frey, J-M Breguet, J. Michler, Dynamic plasticity and failure of microscale glass: rate-dependent ductile-brittle-ductile transition, Nano Letters 19 (2019) 2350-2359